How to Homogenize the Heating Element Design Data

The following describes how to use the JHomogenizer tool to homogenize a map comprised of diffusivity data in a well in a microarray in a heating element design problem. The map has distinct diffusivity values as shown in the figure below.

The following describes how to create a 8x8 grid of homogenized values from the original 128x128 grid of original heterogeneous values. This means solving a total of 64 local problems using the homogenization methods.

• If the JHomogenizer interface is not running, start up the interface.
• The map can be loaded into the JHomogenizer interface or clicking on the Load Map or the Import Map buttons. Then load in the map from the well.map file. This file comes along with the JHomogenizer tool and can be found in the data set. The data set can also be downloaded the link above.
• The next step is to set the homogenized grid size. The values in the Homog Input text fields. The values in the x and y coordinate boxes should be changed to 8. The heterogeneous input boxes should show 128, 128, and 1. Thus the homogenization problems will each be defined on a 16 by 16 grid.
• The next step is to choose a homogenization methods in the list and click in the item. The item should be highlighted.
• Finally, click on the Homogenize! button. The interface will start the calculations and the status will be shown in the Status: line near the bottom of the interface. You will be prompted for a map name for the result of the homogenization process. Enter the name in the dialog and type a carriage return or click on the Okay button.
• You can display the values by clicking on the map in the map list and then you click on Display Values button. The values will be displayed in the text window. The values from the HomCode choice should be the those shown on the Heating Element Design Data web page.
• Once this is done, other methods can be applied to the initial map by clicking on the map in the map list. In our example, click on invertedL. Then click on another homogenization method choice and finally click on the Homogenize! button. To display the new values, click on the Display Values button.

We can also create an output image of the map using the MapEditor tool. To do this do the following.

• Start up the MapEditor tool.
• Once the map is loaded into the display area, click on the Create PPM File. The interface will write a ppm file that contains an image of the map. The name of the file is map.ppm.
• The ppm file can easily be translated into other graphics formats using xview or other image editing software.

Finally, you can save the map data and all of the homogenized results by clicking on the Save Maps button. The data will be stored in a folder with the same name as the name of the file. All of the homogenized results will be stored in subfolders of the original folder.

To reload the data you can use the instructions in some of the other examples. These instructions will not be repeated here.

• If the JHomogenizer interface is not running, start up the interface.
• The map can be loaded into the JHomogenizer interface or clicking on the Load Map or the Import Map buttons. Then load in the map from the well.map file. This file comes along with the JHomogenizer tool and can be found as described above.
• Open the MapEditor tool by clicking on the Show MapEditor button. The Heating Element Design data should appear.
• Click on the Create HTML File button in the MapEditor tool. A file named map.html will be created in the same folder where the well.map file resides.